Select the correct plot of radial probability function `(4pir^(2)R^(2))` for 2s - orbital.

Options

A.
B.
C.
D.

Answer

To determine the correct plot of the radial probability function \(4\pi r^2 R^2\) for the 2s orbital, we need to follow these steps:

### Step 1: Understand the Radial Probability Function
The radial probability function is given by \(4\pi r^2 R^2\), where \(R\) is the radial wave function. This function describes the probability of finding an electron at a distance \(r\) from the nucleus.

### Step 2: Identify Quantum Numbers for 2s Orbital
For the 2s orbital:
- The principal quantum number \(n = 2\)
- The azimuthal quantum number \(l = 0\)

### Step 3: Calculate the Number of Radial Nodes
The number of radial nodes can be calculated using the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]
Substituting the values:
\[ \text{Number of radial nodes} = 2 - 0 - 1 = 1 \]
This means the 2s orbital has 1 radial node.

### Step 4: Analyze the Options
Now, we need to analyze the given options to find the plot that has exactly 1 radial node:
- **Option A**: No radial node (not correct)
- **Option B**: 1 radial node (potentially correct)
- **Option C**: 2 radial nodes (not correct)
- **Option D**: 3 radial nodes (not correct)

### Step 5: Conclusion
Since only **Option B** has exactly 1 radial node, it is the correct plot for the radial probability function of the 2s orbital.

### Final Answer
The correct plot of the radial probability function for the 2s orbital is **Option B**.

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